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Chapter 2: Fundamentals of Statistics
Lecture 16: Populations, samples, models, and
statistics
Appilcation
One or a series of random experiments is performed.
Some data from the experiment(s) are collected.
Planning experiments and collecting data (not discussed in the
textbook).
Data analysis: extract information from the data, interpret the
results, and draw some conclusions.
Descriptive data analysis
Summary measures of the data, such as the mean, median,
range, standard deviation, etc., and some graphical displays, such
as the histogram and box-and-whisker diagram, etc.
It is simple and requires almost no assumptions, but may not allow
us to gain enough insight into the problem.
UW-Madison (Statistics)
Stat 709 Lecture 16
September 2, 2011
1 / 13

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Statistical inference and decision theory
We focus on more sophisticated methods of analyzing data:
statistical inference
and
decision theory
.
The data set is a realization of a random element defined on a
probability space
(Ω
,
F
,
P
)
P
is called the
population
.
The data set or the random element that produces the data is
called a
sample
from
P
.
The size of the data set is called the
sample size
.
Our task
A population
P
is
known
iff
P
(
A
)
is a known value for every event
A
∈
F
.
In a statistical problem, the population
P
is at least partially
unknown.
We would like to deduce some properties of
P
based on the
available sample.
UW-Madison (Statistics)
Stat 709 Lecture 16
September 2, 2011
2 / 13

logo
Statistical inference and decision theory
We focus on more sophisticated methods of analyzing data:
statistical inference
and
decision theory
.
The data set is a realization of a random element defined on a
probability space
(Ω
,
F
,
P
)
P
is called the
population
.
The data set or the random element that produces the data is
called a
sample
from
P
.
The size of the data set is called the
sample size
.
Our task
A population
P
is
known
iff
P
(
A
)
is a known value for every event
A
∈
F
.
In a statistical problem, the population
P
is at least partially
unknown.
We would like to deduce some properties of
P
based on the
available sample.